On Oct 25, 2007, at 2:04 PM, Jack Sarfatti wrote:
Texture defects in 3D space are non-trivial mappings of the 3 sphere S3 with three independent Goldstone phases and four real Higgs scalar fields (Rocky Kolb's "WD40") of third homotopy group.
My theory in 3D space of GMD point defects is S2 of second homotopy group - a sub-case of S3. A GMD texture is a richer defect structure than a GMD field monopole point node of three real Higgs scalars where two world hologram Goldstone phases are undefined (Michael Berry).
The sequence of defects is
domain walls (zero homotopy)
vortex line strings (first homotopy)
point monopoles (second homotopy)
textures (third homotopy)
you can think of these as BRANES
my full theory
has 8 Goldstone phase 0-forms Theta^I & Phi^Jwith 9 real Higgs - one for each dimension of space (not time).
A^I = M^I^I
M^I^J = (dTheta^I)/\(Phi^J) - (Theta^I)/\(dPhi^J)
e^I = I^I + @A^I is tetrad IT
using Rovelli's notation, where in one of my sub-models
@ = N^-1/3
N = # Bekenstein BITS of the World Hologram
ds^2 = e^IeI(LIF) = guv(LNIF)dx^udx^v
i.e. Equivalence Principle of Einstein - the corner stone of the Temple of Space-Time Physics
You can think of a texture as a projection of a defect in a 4D space down to 3D space.
i.e. 4D + 1 space-time down to 3D+1 space time.
Locally gauging 10-parameter Poincare group naturally leads to this picture.
Remember in my picture mesons are pairs of point defects of second homotopy in the GMD(GeoMetroDynamic) field connected by a string vortex defect of first homotopy.
Nucleons are three GMD monopoles connected by vortex strings. These are Bohm hidden
variables guided by QBIT pilot waves. The IR limit of the vortex string short-range strong
Salam gravity induced by residual dark matter zero point energy per Sakharov 1967 has
and effective "Newtonian" potential energy per unit mass of
V(IR) = c^2/Lp* QUARK CONFINEMENT
Lp* = (Lp^2(Newton)(retro-causal future dark energy de Sitter horizon radius) ~ 1 fermi ~ 1Gev
Spin of hadronic resonances ~ (1Gev)^-2(Energy)^2 + zero energy intercept
The UV limit is
V(UV) = c^2r/Lp*^2 ASYMPTOTIC FREEDOM
r = separation of the two GMD point monopoles
Pretty damn simple!
This is like Michael Faraday would have done it. ;-)